Question

Adult tickets to an amusement park cost x dollars. Children's tickets cost y dollars. The Henson family bought 3 adult and 1 child tickets for $207. The Garcia family bought 2 adult and 3 child tickets for $201.

Answer 1

Answer:

Adult tickets (x) were bought for $45 while children tickets (y) at $28

Step-by-step explanation:

Complete question

(Adult tickets to Space City amusement park cost x dollars. Children's tickets cost y dollars. The Henson family bought 3 adult and 1 child tickets for $163. The Garcia family bought 2 adult and 3 child tickets for $174. a. Write equations to represent the Hensons' cost and the Garcias' cost. Hensons' cost: _, Garcias' cost: _. b. Solve the system. adult ticket price: _. Child ticket price:)

a).

Henson's family bought 3 adult tickets and 1 child ticket for $163

3x + y = 163.

Garcia's family bought 2 adult tickets and 3 children tickets for $174

2x + 3y = 174

Equations to represent their cost =

3x + y = 163 ......equation (i)

2x + 3y = 174 .......equation (ii)

b) solving the equation,

This is a simple simultaneous equation and would require any of the methods used to solve simultaneous equations either

1. Substitution method or

2. Eliminatation method.

I'll use substitution method to solve this.

3x + y = 163 .... equation (i)

2x + 3y = 174 .....equation (ii)

From equation (i)

3x + y = 163

Make y the subject of formula

y = 163 - 3x.....equation (iii)

Put y = 163 - 3x into equation (ii)

2x + 3(163 - 3x) = 174

2x + 489 - 9x = 174

Collect like terms

2x - 9x = 174 - 489

-7x = -315

x = 45.

Put x = 45 into equation (i) to solve for y

3(45) + y = 163

135 + y = 163

y = 163 - 135

y = 28.

The cost of the adult tickets is $45 while that of the children is $28